I disagree. 'Mathematical maturity', to me, means: There is no specific advanced prerequisite knowledge, but you need to be able to follow something technical.

As an example: you'd reasonably expect a student with mathematical maturity to know what a set, the Cartesian product of two sets, and a function are. That's high school level math.

From there you can define a ring and a module over a ring, in like 5 mins.

So at that point the Prof, strictly speaking, told you everything you need to know to start studying modules.

Of course, many students will be like whaaaaaa?! When a ring is defined. But here's the point: Mathematical maturity does not mean that you already know what a ring is, but when the Prof defines a ring, you are following along.

Anyway, my point is that there is nothing specific that you need to know.